Primality proof for n = 152083:
Take b = 2.
b^(n-1) mod n = 1.
71 is prime.
b^((n-1)/71)-1 mod n = 31445, which is a unit, inverse 95148.
17 is prime.
b^((n-1)/17)-1 mod n = 110722, which is a unit, inverse 150774.
(17 * 71) divides n-1.
(17 * 71)^2 > n.
n is prime by Pocklington's theorem.